Improved lattice QCD with quarks: the 2 dimensional case

QCD in two dimensions is investigated using the improved fermionic lattice Hamiltonian proposed by Luo, Chen, Xu, and Jiang. We show that the improved theory leads to a significant reduction of the finite lattice spacing errors. The quark condensate and the mass of lightest quark and anti-quark bound state in the strong coupling phase (different from t'Hooft phase) are computed. We find agreement between our results and the analytical ones in the continuum.Comment: LaTeX file (including text + 10 figures

q-Apostol–Euler Polynomials and q-Alternating Sums

Basic properties are established and generating functions are obtained for the q -Apostol–Euler polynomials. We define q -alternating sums and obtain q -extensions of some formulas from Integral Transform. Spectr. Funct., 20, 377–391 (2009). We also deduce an explicit relationship between the q -Apostol–Euler polynomials and the q -Hurwitz–Lerch zeta-function.Встановлено основні властивості та твірні функції q-полiномiв Апостола-Ейлера. Визначено q-знакозмінні суми та отримано q-продовження деяких формул з [Integral Transform. Spec. Funct.-2009.-20.-P. 377-391]. Виведено також явне співвідношення між q-поліномами Апостола-Ейлера i q-дзета-функцією Хурвіца-Лерча

Interpolation function of the genocchi type polynomials

The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary positive real parameters. We prove multiplication theorem of these polynomials. Furthermore, we give some identities and applications associated with these numbers, polynomials and their interpolation functions.Comment: 14 page

Monte Carlo Hamiltonian of lattice gauge theory

We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.Comment: "Non-Perturbative Quantum Field Theory: Lattice and Beyond", Guangzhou, China 200

Generalized seniority for the shell model with realistic interactions

The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are treated in the generalized seniority scheme, for generalized seniority v<=3. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell model space.Comment: 13 pages, 8 figures; published in Phys. Rev.